The colored HOMFLYPT function is $q$-holonomic
Geometric Topology
2018-05-31 v2 High Energy Physics - Theory
Abstract
We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a -holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an super-polynomial of knots in 3-space, as was conjectured by string theorists. Our proof uses skew Howe duality that reduces the evaluation of web diagrams and their ladders to a Poincare-Birkhoff-Witt computation of an auxiliary quantum group of rank the number of strings of the ladder diagram.
Cite
@article{arxiv.1604.08502,
title = {The colored HOMFLYPT function is $q$-holonomic},
author = {Stavros Garoufalidis and Aaron D. Lauda and Thang T. Q. Lê},
journal= {arXiv preprint arXiv:1604.08502},
year = {2018}
}
Comments
38 pages